The usual symmetries (space-time translations and spatial rotations) are fairly well discussed in the literature, including additional steps such as the symmetrization of the energy-momentum tensor [1]}. For instance, in terms of the electric field \(E_i = - F_{0i}\)  and the magnetic field \(B_i = - (1/2)\,\varepsilon _{ijk}\,F^{jk}\) , where \(\varepsilon _{ijk}\)  is the 3-dimensional Kronecker symbol, for time-translations (only \(a^0 = 1\)  is non-zero) one finds
\(J^0 = \frac{1}{2}\,(E^2 + B^2) + \nabla \cdot (A_0\,{\bf E}) - A_0\,\nabla \cdot {\bf E} \,. \nonumber \) 
